Kinetic theory of quasi-stationary collisionless axisymmetric plasmas in the presence of strong rotation phenomena

Abstract

The problem of formulating a kinetic treatment for quasi-stationary collisionless plasmas in axisymmetric systems subject to the possibly independent presence of local strong velocity-shear and supersonic rotation velocities is posed. The theory is developed in the framework of the Vlasov-Maxwell description for multi-species non-relativistic plasmas. Applications to astrophysical accretion discs arising around compact objects and to plasmas in laboratory devices are considered. Explicit solutions for the equilibrium kinetic distribution function (KDF) are constructed based on the identification of the relevant particle adiabatic invariants. These are shown to be expressed in terms of generalized non-isotropic Gaussian distributions. A suitable perturbative theory is then developed which allows for the treatment of non-uniform strong velocity-shear/supersonic plasmas. This yields a series representation for the equilibrium KDF in which the leading-order term depends on both a finite set of fluid fields as well as on the gradients of an appropriate rotational frequency. Constitutive equations for the fluid number density, flow velocity, and pressure tensor are explicitly calculated. As a notable outcome, the discovery of a new mechanism for generating temperature and pressure anisotropies is pointed out, which represents a characteristic feature of plasmas considered here. This is shown to arise as a consequence of the canonical momentum conservation and to contribute to the occurrence of temperature anisotropy in combination with the adiabatic conservation of the particle magnetic moment. The physical relevance of the result and the implications of the kinetic solution for the self-generation of quasi-stationary electrostatic and magnetic fields through a kinetic dynamo are discussed. V C 2013 AIP Publishing LLC. [http://dx.

Acceleration of the charged particles due to chaotic scattering in the combined black hole gravitational field and asymptotically uniform magnetic field

“…Such condition could be represented in the kinetic approach [4]. Large velocities with γ z 1 can be obtained for properly chosen initial conditions, but the question arise, if such conditions could be represented by realistic astrophysical conditions.…”

“…However, the motion of the charged test particles in the close vicinity of a black hole horizon could be strongly influenced even by relatively weak test magnetic fields [29]. For a charged test particle with charge q and mass m moving in the vicinity of a black hole with mass M surrounded by an uniform magnetic field of the strength B, one can introduce a dimensionless quantity b that can be identified as relative Lorenz force [24] b = |q|BG M/mc 4 . This quantity can be really quite large even for weak magnetic fields due to the large value of the specific charge q/m.…”

“…Many of the observed black hole candidates are assumed to have an accretion disc constituted from conducting plasma which dynamics can generate a regular magnetic field. The kinetic effects of collisionless plasmas could generate equilibrium configurations of plasmas in various conditions under combined gravitational and magnetic fields [3][4][5] or could govern transitions from neutral to ionized equilibria of accretion discs [6].…”

Covariant formulation of spatially non-symmetric kinetic equilibria in magnetized astrophysical plasmas

“…This occurs in particular in the presence of temperature and pressure anisotropies, local flows, such as diamagnetic flow velocities, finite Larmor-radius (FLR), and energy-correction effects. [35][36][37][38][39][40][41][42] A qualitative feature of astrophysical magnetized plasmas is related to the occurrence of kinetic plasma regimes, which persist for long times (with respect to the observer and/or plasma characteristic times), despite the presence of macroscopic time-varying phenomena of various origin, such as flows, non-uniform gravitational/EM fields, and EM radiation, 43 possibly including that arising from singleparticle radiation-reaction processes. [4][5][6][7][8][9][10][11] It is argued that, for collisionless plasmas, these states might actually correspond-at least locally and in a suitable asymptotic senseto some kind of kinetic equilibrium, which characterizes the species KDFs.…”

“…In fact, analogous conclusions apply in principle both to astrophysical and laboratory systems, 35,36 ranging from non-axisymmetric and rotating accretion-disc plasmas, localized non-axisymmetric plasma flows in astrophysical plasmas (such as jets and star flares), as well as Laboratory plasmas (such as Tokamak, RFP and Stellarator systems), all characterized by the presence of a rich phenomenology. 40 The study of plasma dynamics in high-energy astrophysical scenarios has gained interest in the last years among the scientific community, thanks to the development of accurate and advanced numerical tools able to investigate in greater details the physical phenomena occurring in these systems (see, for example, Refs. [45][46][47][48][49][50][51][52].…”